Question 1:
We are given the tension force T=58.5 N and we need to find the weight(w) of the child and the normal force(N) acting on the sled.
Using Newton's second law, we can write the equations for the forces acting along the parallel(perpendicular) direction to the inclined plane:
T - w*sin(theta) = 0
N - w*cos(theta) = 0
Here, theta is the angle between the inclined plane and the horizontal. It is given that theta = 30°.
Using the first equation, we can find the weight of the child:
w*sin(30) = 58.5
w = 58.5/sin(30)
w = 58.5/0.5
w = 117 N
Therefore, the weight of the child is 117 N.
Now, using the second equation to find the magnitude of the normal force acting on the sled:
N = w*cos(30)
N = 117*cos(30)
N = 117*0.866
N ≈ 101.3 N
Therefore, the normal force acting on the sled is approximately 101.3 N.
Question 2:
(a) To find the angle the ramp makes with respect to the horizontal, we use the formula for acceleration along an inclined plane without friction:
a = g*sin(theta)
Where a is the acceleration, g is the acceleration due to gravity (9.81 m/s^2), and theta is the angle. We are given a=4.50 m/s^2.
theta = arcsin(a/g)
theta = arcsin(4.50/9.81)
theta ≈ 27.5°
The angle the ramp makes with respect to the horizontal is approximately 27.5°.
(b) To find the time it takes the puck to reach the bottom, we can use the formula:
s = 0.5*a*t^2
Where s is the length of the ramp, a is the acceleration, and t is the time. We are given s = 5.80 m and a = 4.50 m/s^2.
5.80 = 0.5 * 4.50 * t^2
t^2 = 5.80/(0.5 * 4.50)
t^2 ≈ 2.58
t ≈ 1.61 s
It takes the puck approximately 1.61 seconds to reach the bottom of the ramp.
(c) If the mass of the puck is doubled, the acceleration down the ramp will remain the same. This is because the gravitational force acting on the puck is directly proportional to its mass, so doubling the mass will double the gravitational force. However, the normal force acting on the puck will also double. Since these two forces are balanced, the acceleration remains unchanged. Thus, the new acceleration down the ramp is the same as before:
New acceleration = 4.50 m/s^2
Question 1:
Suppose a child of weight w climbs onto the sled. If the tension force is measured to be 58.5 N, find the weight of the child and the magnitude of the normal force acting on the sled.
Question 2 :
(a) Suppose a hockey puck slides down a frictionless ramp with an acceleration of 4.50 m/s2. What angle does the ramp make with respect to the horizontal?
°
(b) If the ramp has a length of 5.80 m, how long does it take the puck to reach the bottom?
s
(c) Now suppose the mass of the puck is doubled. What's the puck's new acceleration down the ramp?
m/s2
1 answer
1 answer