a student could either pull or push , at an angle of 30 deg from the horizontal, a 50-kg crate on a horizontal surface, where the coefficient of kinetic friction between the crate and the surface is .20 the crate is to be moved a horizontial distance of 15-m (a) compared to pushing pulling requires (1) less (2) the same or, (3) more work (b)calculate the minimum work required for both pulling and pushing
a) the same
b) M g cos 30 * (0.2) * 15 m. That is the work required to move it slowly without accelerating it.
To determine whether pushing or pulling requires more work, we need to compare the work done in each case. The work done is given by the formula:
Work = Force * Distance * cos(theta)
where:
- Force is the horizontal force applied (in this case, either pushing or pulling)
- Distance is the distance the crate is moved horizontally
- theta is the angle between the force and the horizontal direction
In this scenario,
- The crate has a mass of 50 kg.
- The coefficient of kinetic friction between the crate and the surface is 0.20.
- The angle between the applied force and the horizontal is 30 degrees.
- The horizontal distance the crate needs to be moved is 15 m.
Now, let's determine the minimum work required for both pushing and pulling.
(a) To determine if pushing or pulling requires more work, we need to compare the forces. Since the force remains the same in both cases, the work done will be equal if the angle is the same.
θ = 30 degrees in both cases.
Therefore, pushing and pulling require the same amount of work.
(b) Now, we need to calculate the minimum work required in both cases.
For pushing:
- Force = Normal force (Fn) - Frictional force (Ff)
- Fn = mass * gravity
- Ff = coefficient of kinetic friction * Fn
For pulling:
- Force = Applied force (Fa) + Frictional force (Ff)
First, let's calculate the necessary forces:
- Normal force (Fn) = mass * gravity = 50 kg * 9.8 m/s^2 = 490 N
- Frictional force (Ff) = coefficient of kinetic friction * Fn = 0.20 * 490 N = 98 N
For pushing:
- Work = Force * Distance * cos(theta)
- Work = (Fn - Ff) * Distance * cos(30 degrees)
- Work = (490 N - 98 N) * 15 m * cos(30 degrees)
For pulling:
- Work = Force * Distance * cos(theta)
- Work = (Fa + Ff) * Distance * cos(30 degrees)
- Work = (Fa + 98 N) * 15 m * cos(30 degrees)
Now, you can calculate the minimum work required for both pushing and pulling using the above formulas and the given values.