The force needed to accelerate a mass of 40 kg from velocity v₁ = (4î - 5) + 3k)m/s to v = (8î + 3) - 5k)m/s in 10 seconds is 12.4 N.
Start by calculating the change in velocity (Δv) experienced by the object. This can be done by subtracting the initial velocity v₁ from the final velocity v.
Δv = v - v₁ = ((8î + 3) - 5k) - ((4î - 5) + 3k)
= 8î + 3 - 5k - 4î + 5 - 3k
= 4î - 8k + 8
Next, calculate the acceleration (a) using the formula:
a = Δv / t
where t is the time interval, given as 10 seconds.
a = (4î - 8k + 8) / 10
= (0.4î - 0.8k + 0.8) m/s²
The force (F) required to accelerate the object can be found using Newton's second law:
F = m * a
where m is the mass, given as 40 kg.
F = (40 kg) * (0.4î - 0.8k + 0.8) m/s²
= (16î - 32k + 32) N
Simplify the expression to obtain the final answer:
F = 16î - 32k + 32 N
≈ 12.4 N
Therefore, the force needed to accelerate a mass of 40 kg from velocity v₁ = (4î - 5) + 3k)m/s to v = (8î + 3) - 5k)m/s in 10 seconds is approximately 12.4 N.
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On a sunny spring day, Mr. Hane’s family went to a zoo in his town. His daughter looked at an elephant, and she found that the mass of the elephant is 2019 kg. What is the weight of the elephant in Newtons? Use the acceleration due to gravity (g) as 9.8 meters per second squared.
The weight of the elephant is approximately 19,780.2 Newtons, calculated by multiplying its mass (2019 kg) by the acceleration due to gravity (9.8 m/s²).
To calculate the weight of the elephant in Newtons, we need to use the formula:
Weight = Mass x Acceleration due to gravity
Given that the mass of the elephant is 2019 kg and the acceleration due to gravity is 9.8 m/s^2, we can substitute these values into the formula:
Weight = 2019 kg x 9.8 m/s^2
By multiplying these values, we find that the weight of the elephant is approximately 19,780.2 Newtons.
The weight of an object is the force with which it is attracted towards the center of the Earth due to gravity. The unit of weight is Newtons, and it represents the force required to support the object against gravity. In this case, the weight of the elephant tells us the force exerted by the Earth on the elephant, and it is approximately 19,780.2 Newtons.
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Equation of path of projectile is y=x(1-x)
The equation of the path of a projectile is y = x(1 - x). Projectile motion is the movement of an object in a parabolic trajectory as a result of being propelled or released under the influence of gravity. A projectile, in simple terms, is any object that is launched into the air, such as a bullet, a baseball, or a rock. It's important to note that the parabolic trajectory is due to the force of gravity acting on the object.
To better understand projectile motion, we must first examine the horizontal and vertical components of motion. The horizontal component of motion is constant, indicating that there is no acceleration in that direction. The vertical component, on the other hand, has acceleration because of gravity. The parabolic trajectory is the result of these two components of motion.As the projectile is launched, it travels a certain distance horizontally before beginning to descend as a result of gravity's influence, resulting in a parabolic path.The general formula for the trajectory of a projectile in two dimensions is given by:y = xtanθ - (gx²) / 2(v₀cosθ)²Where:y is the vertical distance covered by the projectilex is the horizontal distance covered by the projectileθ is the angle of projectiong is the acceleration due to gravityv₀ is the initial velocity of the projectile In the case of the given equation, y = x(1 - x), the path of the projectile will be a parabolic trajectory with a vertex at x = 0.5 and y = 0.25. The equation represents the projectile's vertical distance, y, as a function of its horizontal distance, x. It is crucial to note that the projectile's initial velocity and angle of projection are not considered in this equation.For such more question on acceleration
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A conducting sphere (radius a) is placed at the center of a conducting spherical shell (inner radius b and outer radius c). The conductors are in electrostatic equilibrium.
The sphere has a net charge of +5.10 μC and the shell has a net charge of +5.10 μC. What is the charge on the inner surface of the shell? answer in μC
The inner sphere has a net charge of +5.10 μC and the shell has a net charge of +5.10 μC. What is the charge on the outer surface of the shell? answer in μC
Charge on inner surface: -5.10 μC
Charge on outer surface: +10.20 μC
In electrostatic equilibrium, the charges on conductors distribute in such a way that the electric field inside them is zero. Given a conducting sphere with a net charge of +5.10 μC placed at the center of a conducting spherical shell with inner radius b and outer radius c, we can determine the charges on the inner and outer surfaces of the shell.
1. Charge on the inner surface of the shell:
Since the electric field inside the conductor is zero, the charges on the inner surface of the shell will redistribute in such a way that they cancel out the electric field from the sphere at the center.
Since the net charge on the sphere is +5.10 μC, the inner surface of the shell will have an equal and opposite charge to neutralize the electric field from the sphere. Therefore, the charge on the inner surface of the shell is -5.10 μC.
2. Charge on the outer surface of the shell:
The total charge on the shell is +5.10 μC, which means the sum of the charges on the inner and outer surfaces of the shell must equal this value.
Since the charge on the inner surface is -5.10 μC, the charge on the outer surface can be calculated as the difference:
Charge on the outer surface = Total charge on the shell - Charge on the inner surface
Charge on the outer surface = +5.10 μC - (-5.10 μC)
Charge on the outer surface = +10.20 μC
Therefore, the charge on the inner surface of the shell is -5.10 μC, and the charge on the outer surface of the shell is +10.20 μC.
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A rigid circular loop has a radius of 0.20 m and is in the xy-plane. The loop carries a
clockwise current I. The magnitude of the magnetic moment of the loop is 0.75 A.m2
.
A uniform external magnetic field, B = 0.20 T is directed parallel to the plane of the
loop. An external torque changes the orientation of the loop from one of lowest potential energy to one of highest potential energy. Calculate the work done by this external
torque.
A rigid circular loop having a radius of 0.20 m and is in the xy-plane, carries a uniform external magnetic field. B = 0.20 T and is directed parallel to the plane of the loop. The torque exerted on the loop is given by the formula as follows;τ = NABsin θ
Where τ is the torque, N is the number of turns, A is the area of the loop, B is the magnetic field strength, and θ is the angle between the normal to the loop and the magnetic field direction. The direction of the torque is given by the right-hand rule and depends on the direction of the magnetic field.To obtain the magnitude of the torque, we need to evaluate all the terms in the formula, τ = NABsinθ.A = πr² = π (0.20 m)² = 0.1257 m²The angle between the normal to the loop and the magnetic field direction is 0 degrees since the field is parallel to the loop.θ = 0°Substituting the values in the formula, we have;τ = NABsinθ= N (0.1257 m²) (0.20 T) (sin 0°)τ = 0 NmThe torque exerted on the loop is zero since the angle between the normal to the loop and the magnetic field direction is zero. The torque only exists when there is an angle between the normal and the magnetic field direction. Therefore, there is no net force on the current loop.For such more question on torque
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A 50.0-kg wagon is pulled with a constant force of 380 N. Neglecting friction, the wagon's acceleration will be
A 50.0-kg wagon is pulled with a constant force of 380 N. Neglecting friction, the wagon's acceleration will be 7.6 m/s².
When a constant force acts on a wagon, it causes the wagon to accelerate We can calculate the wagon's acceleration using Newton's second law, which states that the force acting on an object is directly proportional to its acceleration, and the acceleration is inversely proportional to the mass of the object.A = F/mHere,A = AccelerationF = Force acting on the wagon m = mass of the wagon Substituting the given values, we getA = 380 N/50.0 kgA = 7.6 m/s²Therefore, the acceleration of the wagon is 7.6 m/s² when it is pulled with a constant force of 380 N, neglecting friction.For such more question on Newton's second law
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why is it considered that all electric charges are multiples of e
Answer:
electric charges are quantised
Explanation:
which means they exist as integral multiples q=ne . this was practically proved by the Millikan's oil drop experiment in which he let charged oil droplets as fine as mist fall under the effect of gravity, after measuring the charge on many drops the results showed that charges were multiples of a minimum value 1.6 x 10[tex]{-19}[/tex] which we now know as the charge on an electron or elementary charge.
The student has a mass of 50.0 kg. What is her momentum at 2 s (in kgm/s)?
Answer:
50kgm/2
Explanation:
A new ride being built at an amusement park includes a vertical drop of 79.8 meters. Starting from rest, the ride vertically drops that distance before the track curves forward. If friction is neglected, what would be the speed of the roller coaster at the bottom of the drop?
Answer:
Approximately [tex]39.6\; {\rm m\cdot s^{-1}}[/tex] (assuming that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex].)
Explanation:
Under the assumptions, vertical acceleration of the vehicle during the ride would be equal to the gravitational field strength: [tex]a = g = 9.81\; {\rm m\cdot s^{-2}}[/tex].
Apply the following SUVAT equation to find the velocity of the vehicle at the bottom of the drop:
[tex]v^{2} - u^{2} = 2\, a\, x[/tex],
Where:
[tex]v[/tex] is the final velocity at the bottom of the drop;[tex]u[/tex] is the initial velocity at the beginning of the drop; [tex]u = 0\; {\rm m\cdot s^{-1}}[/tex] since the vehicle started from rest;[tex]a = g = 9.81\; {\rm m\cdot s^{-2}}[/tex] is the vertical acceleration of the vehicle during the drop;[tex]x = 79.8\; {\rm m}[/tex] is the vertical displacement of the vehicle during the drop.Rearrange this equation to find [tex]v[/tex]:
[tex]\begin{aligned}v &= \sqrt{u^{2} + 2\, a\, x} \\ &\approx \sqrt{0^{2} + 2\, (9.81)\, (79.8)} \; {\rm m\cdot s^{-1}} \\ &\approx 39.6\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].
Hence, the speed of this vehicle at the bottom of the drop would be approximately [tex]39.6\; {\rm m\cdot s^{-1}}[/tex].
A small sphere with charge 0.850 μC is placed at the center of a cube. What is the electric flux through one surface of the cube? answer in N⋅m2/C
The electric flux through the cube's surface is approximately 9.60 × 10⁵ N⋅m²/C.
To calculate the electric flux through one surface of a cube due to a charge at its center, we can apply Gauss's Law. Gauss's Law states that the electric flux (Φ) through a closed surface is equal to the enclosed charge (Q) divided by the electric constant (ε₀).
1. Calculate the electric flux:
The electric flux through one surface of the cube can be determined by considering a Gaussian surface that encloses the charge at the center. Since the cube is symmetrical, we choose a cube of the same size as our Gaussian surface.
The enclosed charge (Q) is the charge of the small sphere, which is 0.850 μC.
The electric constant (ε₀) is a fundamental constant equal to approximately 8.854 × 10⁻¹² N⋅m²/C².
Using Gauss's Law, the electric flux is given by:
Φ = Q / ε₀
Φ = (0.850 μC) / (8.854 × 10⁻¹² N⋅m²/C²)
2. Calculate the electric flux in N⋅m²/C:
Substituting the values into the equation:
Φ ≈ (0.850 × 10⁻⁶ C) / (8.854 × 10⁻¹² N⋅m²/C²)
Φ ≈ 9.60 × 10⁵ N⋅m²/C
Therefore, the electric flux through one surface of the cube due to the charge at its center is approximately 9.60 × 10⁵ N⋅m²/C.
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17. The time taken by a 100 g stone to reach the ground when dropped from the top of (A) your school building has been given. Write a suitable formula for the calculation of ght of your school building.
