A student in a lab exerts a 14 N force to pull a block a distance of 63 cm. If a total of 8 J of work is done, the angle between the force and the displacement is
none of the above
89°
25°
61°
65°
A 1.6-kg block is dropped from 66 cm above a spring in equilibrium. The force constant for the spring is 142 N/m. Calculate the maximum compression in the spring.
work = force (in direction of motion) X distance
W = (F cos t) x
cos t = W/Fx
t = arccos(W/Fx) = arccos [8/(14)(0.63)] = arccos 0.907 = 24.9 = 25 degrees
To find the angle between the force and the displacement, we need to use the work-energy principle. The work done is given as 8 J, which can be calculated using the formula:
Work = Force * Distance * cos(theta)
Here, the force is 14 N and the distance is 63 cm. We need to find the angle theta.
Let's rearrange the formula to solve for cos(theta):
cos(theta) = Work / (Force * Distance)
cos(theta) = 8 J / (14 N * 63 cm)
Before we proceed, it's important to convert the distance from centimeters to meters, as the SI unit for force is Newtons (N) and for distance is meters (m).
1 m = 100 cm
So, the distance is: 63 cm * (1 m / 100 cm) = 0.63 m
Substituting the values, we get:
cos(theta) = 8 J / (14 N * 0.63 m)
cos(theta) ≈ 0.1017
To find the angle, we can take the inverse cosine (cos^(-1)) of this value:
theta ≈ cos^(-1)(0.1017)
Using a calculator, we find:
theta ≈ 84.9°
Therefore, none of the given options are correct. The angle between the force and the displacement is approximately 84.9°.