A 5.3-kg block is pushed 2.3 m up a vertical wall with constant speed by a constant force of magnitude F applied at an angle of θ = 30° with the horizontal, as shown in the figure below. If the coefficient of kinetic friction between block and wall is 0.30, determine the following.
(a) the work done by F
J
(b) the work done by the force of gravity
J
(c) the work done by the normal force between block and wall
J
(d) By how much does the gravitational potential energy increase during the block's motion?
J
im getting wrong answer for 1) i got 216.2 J but that is incorrect
2) im also getting wrong when i plug in everything.
3) is 0
4) is 119.50
so can u please look at 1 and 2 and help me
a) F sin30= mg + Ff
so we need to find Ff
Fn = F cos30 = Ff/mu
so Ff = mu F cos30
substitute
F sin30 = mg + mu F cos30
solve for F
F sin30 d = W
b) W = mgh = 5.3*9.8*2.3 (same as d)
c) Normal force can NEVER do work
Late, I know, but
b] W = -mgh, not mgh. Ran into this problem myself. :/
To solve this problem, we need to consider the different forces acting on the block and use the work-energy principle. Let's calculate each part step by step:
(a) The work done by the applied force F:
The work done is given by the formula: Work = Force * Distance * cos(θ), where θ is the angle between the force and displacement. In this case, the force F is applied at an angle of 30° with the horizontal, so the angle between the force and displacement is also 30°. Given that the distance is 2.3 m and the force magnitude is not mentioned in the question, we cannot determine the exact value of the work done by F without additional information.
(b) The work done by the force of gravity:
The work done by the force of gravity is equal to the change in gravitational potential energy. It is given by the formula: Work = m * g * h, where m is the mass of the block, g is the acceleration due to gravity (9.8 m/s^2), and h is the vertical displacement. In this case, since the block is being pushed vertically upwards, the vertical displacement is positive. Therefore, the work done by gravity is Work = 5.3 kg * 9.8 m/s^2 * 2.3 m = 122.94 J.
(c) The work done by the normal force between the block and the wall:
The work done by the normal force is zero because the normal force acts perpendicular to the displacement, and the work done by a force is zero when the force is perpendicular to the displacement.
(d) The increase in gravitational potential energy:
The increase in gravitational potential energy is equal to the work done by the force of gravity, which we have already calculated. Therefore, the increase in gravitational potential energy is 122.94 J.
Based on the given information and calculations provided, it seems that there may be some errors in the calculations. Please double-check your calculations for parts (a) and (b) to identify any potential mistakes.