# Solve Block on an Incline: Net Force, Accel, Speed in 9 m/s

• cstout
In summary, a 11.4-kg block is released from rest on a frictionless track inclined at an angle of 47°. The net force on the block after it is released is zero, as there is no friction. The acceleration of the block is gsin(47°) = 8.78 m/s^2. If the block is released from rest, it will take approximately 1.02 seconds for it to attain a speed of 9 m/s.
cstout
[SOLVED] Block on an incline

A 11.4-kg block is released from rest on a frictionless track inclined at an angle of 47°. (a) What is the net force on the block after it is released? (b) What is the acceleration of the block? (c) If the block is released from rest, how long will it take for the block to attain a speed of 9 m/s?

I have been working on this problem but for some reason I must have an error somewhere, can anyone show me the correct answers.

If you show us your solution we can maybe find the error.

(a) The net force on the block is equal to its weight component down the incline, which can be calculated using the formula F = mgsinθ, where m is the mass of the block, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the incline. Plugging in the values, we get F = (11.4 kg)(9.8 m/s^2)sin(47°) = 79.3 N.

(b) The acceleration of the block can be calculated using Newton's second law, F = ma. Plugging in the net force calculated in part (a), we get 79.3 N = (11.4 kg)a. Solving for a, we get a = 6.96 m/s^2.

(c) To find the time it takes for the block to reach a speed of 9 m/s, we can use the formula v = u + at, where v is the final velocity, u is the initial velocity (which is 0 m/s in this case), a is the acceleration calculated in part (b), and t is the time. Plugging in the values, we get 9 m/s = 0 + (6.96 m/s^2)t. Solving for t, we get t = 1.29 seconds. Therefore, it will take the block 1.29 seconds to reach a speed of 9 m/s.

## What is the formula for calculating net force on a block on an incline?

The formula for calculating net force on a block on an incline is Fnet = mgsinθ, where m is the mass of the block, g is the acceleration due to gravity, and θ is the angle of the incline.

## How do you calculate the acceleration of a block on an incline?

The acceleration of a block on an incline can be calculated using the formula a = gsinθ, where g is the acceleration due to gravity and θ is the angle of the incline.

## What is the speed of a block on an incline with a net force of 9 m/s?

The speed of a block on an incline with a net force of 9 m/s can be calculated using the formula v = at, where a is the acceleration of the block and t is the time it takes for the block to reach that speed.

## What factors can affect the net force on a block on an incline?

The net force on a block on an incline can be affected by the mass of the block, the angle of the incline, and the coefficient of friction between the block and the surface of the incline.

## How does the speed of a block on an incline change as the angle of the incline increases?

As the angle of the incline increases, the speed of the block on the incline will also increase, assuming all other factors remain constant. This is because a larger angle of incline results in a greater component of the force of gravity acting on the block parallel to the incline, causing the block to accelerate and increase in speed.

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