To move a crate across a rough floor, you pull on it at an angle of 21 degrees above the horizontal. How much force is needed if the mass of the crate is 32kg and the coefficient of static friction between the crate and floor is 0.57

F•cosα=Ffriction=k•mg

F=kmg/cosα=0.57•32•9,8/cos 21 =191 N

Mastering Physics said the answer is 240N. NO IDEA HOW

To find the force needed to move the crate across the rough floor, we need to consider the forces acting on the crate and apply Newton's laws of motion.

Let's break down the forces acting on the crate:

1. Weight (mg): This is the force exerted by gravity on the crate and can be calculated by multiplying the mass (m) of the crate by the acceleration due to gravity (g). Here, m = 32 kg and g = 9.8 m/s^2, so the weight of the crate is W = mg.

2. Normal force (N): This is the force exerted by the floor on the crate perpendicular to the surface. It is equal to the weight of the crate when the crate is on a horizontal surface.

3. Force of friction (f): The force of friction opposes the motion of the crate and can be calculated using the coefficient of static friction (μs) and the normal force (N). The static friction force can be represented as f = μs * N.

4. Horizontal force (F): This is the force applied to move the crate across the floor.

Now, let's find the normal force:

Since the crate is on a rough floor, the normal force is still equal to the weight of the crate (N = W = mg). Thus, N = 32 kg * 9.8 m/s^2.

Next, let's find the force of friction:

The force of friction can be calculated using the coefficient of static friction (μs) and the normal force (N). Given that the coefficient of static friction is 0.57, we can calculate the force of friction as follows: f = μs * N.

Finally, let's find the horizontal force needed to move the crate:

Since the horizontal force (F) is applied at an angle of 21 degrees above the horizontal, we can find the horizontal component of the force using trigonometry. The horizontal force (F) is equal to the force of friction (f).

Therefore, to find the force needed to move the crate across the rough floor, we need to calculate the force of friction (f).