A horizontal force of 150 N is used to push a 42.0-kg packing crate a distance of 6.60 m on a rough horizontal surface. If the crate moves at constant speed, find each of the following.
To find each of the following, we can use the formula for work:
Work = Force * Distance
1. Work done by the applied force:
Work = 150 N * 6.60 m
Work = 990 J (joules)
2. Work done by the frictional force:
Since the crate is moving at constant speed, the work done by the frictional force is equal in magnitude but opposite in direction to the work done by the applied force. So, the work done by the frictional force is -990 J.
3. The force of friction:
To find the force of friction, we can use the equation:
Force of friction = applied force - net force
Net force = ma (Newton's second law)
Net force = 42.0 kg * 0 m/s^2 (since it moves at a constant speed)
Net force = 0 N
Therefore, the force of friction is:
Force of friction = 150 N - 0 N
Force of friction = 150 N
4. The coefficient of friction:
To find the coefficient of friction, we can use the equation:
Force of friction = coefficient of friction * normal force
Normal force = mass * gravity
Normal force = 42.0 kg * 9.8 m/s^2
Normal force = 411.6 N
Therefore, the coefficient of friction is:
150 N = coefficient of friction * 411.6 N
coefficient of friction = 150 N / 411.6 N
coefficient of friction ≈ 0.364
To find each of the following quantities, we need to use the given information and apply the appropriate equations. Here are the steps to find the requested values:
1. Find the frictional force:
The frictional force (F_friction) opposes the motion of the crate and can be determined using the equation:
F_friction = μ * F_normal
where μ is the coefficient of friction, and F_normal is the normal force.
2. Find the normal force:
The normal force (F_normal) is the force exerted by the surface on the crate and is equal in magnitude but opposite in direction to the weight of the crate.
F_normal = m * g
where m is the mass of the crate, and g is the acceleration due to gravity (approximately 9.8 m/s²).
3. Find the coefficient of friction:
The coefficient of friction (μ) describes the roughness of the surface and can be determined using the equation:
μ = F_friction / F_normal
Let's apply these steps to find each of the requested quantities.
1. Frictional force (F_friction):
We need to determine the coefficient of friction (μ) to find the frictional force. If the crate is moving at constant speed, it implies that the applied force (150 N) is equal in magnitude and opposite in direction to the frictional force. Therefore:
F_friction = 150 N
2. Normal force (F_normal):
We can determine the normal force by multiplying the mass of the crate (42.0 kg) by the acceleration due to gravity (9.8 m/s²):
F_normal = 42.0 kg * 9.8 m/s²
3. Coefficient of friction (μ):
We can calculate the coefficient of friction by dividing the frictional force (150 N) by the normal force:
μ = 150 N / (42.0 kg * 9.8 m/s²)
By following these steps, you can find the frictional force, normal force, and the coefficient of friction for the given scenario.