# How much work would it take to horizontally accelerate an object with a mass of #8 kg# to #3 m/s# on a surface with a kinetic friction coefficient of #3 #?

The work is

The force of friction is

According to Newton's Second Law

The acceleration is

Apply the equation of motion

The distance is

The work done is

By signing up, you agree to our Terms of Service and Privacy Policy

To calculate the work required to horizontally accelerate an object with a mass of 8 kg to 3 m/s on a surface with a kinetic friction coefficient of 3, you can use the equation:

[ W = \frac{1}{2} m v^2 + f_k d ]

where (W) is the work done, (m) is the mass of the object (8 kg), (v) is the final velocity (3 m/s), (f_k) is the kinetic friction coefficient (3), and (d) is the distance over which the force is applied.

First, you need to find the distance (d) using the equation:

[ f_k = \mu_k N ]

where (\mu_k) is the coefficient of kinetic friction and (N) is the normal force. Since the object is horizontally accelerating, the normal force (N) is equal to the weight of the object, which is (mg), where (g) is the acceleration due to gravity (9.8 m/s²).

[ f_k = \mu_k mg ]

[ d = \frac{v^2}{2\mu_k g} ]

Substitute the given values into the equation:

[ d = \frac{(3, \text{m/s})^2}{2(3)(9.8, \text{m/s}^2)} ]

[ d \approx 0.153, \text{m} ]

Now, you can calculate the work done:

[ W = \frac{1}{2} m v^2 + f_k d ]

[ W = \frac{1}{2}(8, \text{kg})(3, \text{m/s})^2 + (3)(0.153, \text{m}) ]

[ W \approx 36, \text{J} ]

So, it would take approximately 36 joules of work to horizontally accelerate the object to 3 m/s on a surface with a kinetic friction coefficient of 3.

By signing up, you agree to our Terms of Service and Privacy Policy

To horizontally accelerate an object with a mass of 8 kg to 3 m/s on a surface with a kinetic friction coefficient of 0.3, it would take approximately 36 joules of work.

By signing up, you agree to our Terms of Service and Privacy Policy

- What is the work done by a 0.47 N force pushing a 0.026 kg pencil 0.26 m against a force of friction of 0.23N?
- Emily’s vacuum cleaner has a power rating of 200 watts. If the vacuum cleaner does 360,000 joules of work, how long did Emily speed vacuuming?
- If an object with a mass of #5 kg # changes speed from #12m/s# to # 8m/s#, by how much does its kinetic energy change?
- A ball with a mass of #300 g# is projected vertically by a spring loaded contraption. The spring in the contraption has a spring constant of #32 (kg)/s^2# and was compressed by #5/7 m# when the ball was released. How high will the ball go?
- What is an example of an energy transformation from electrical to sound energy?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7