Suppose a child of weigh w climbs into 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?
Weight of the child ___________ N
Normal force on the sled _________ N
I have no idea where the tension is.
To find the weight of the child and the magnitude of the normal force acting on the sled, we can break down the problem into two components: vertical forces and horizontal forces.
First, let's consider the vertical forces. In this case, there are two forces acting vertically: the weight of the child and the normal force on the sled.
The weight of an object can be calculated using the formula:
Weight = mass × acceleration due to gravity
However, in this case, we are given the tension force, not the mass. The tension force is equal to the weight of the child plus the normal force on the sled. So, we can write the equation:
Tension force = Weight of the child + Normal force
Given that the tension force is measured to be 58.5 N, we can substitute this value into the equation:
58.5 N = Weight of the child + Normal force
Now, let's consider the horizontal forces. Since the sled is not accelerating horizontally, there is no net force acting in that direction. This means the tension force is equal to the frictional force opposing the motion, which is equal to the normal force multiplied by the coefficient of kinetic friction.
Since the sled is not moving, the coefficient of kinetic friction is 0 (zero). Therefore, the frictional force is also 0, which implies that the tension force is 0 in the horizontal direction.
Now, we can solve the system of equations to find the weight of the child and the magnitude of the normal force on the sled. Since the tension force is 0 horizontally, we know that the normal force is also 0 horizontally, which means the normal force only acts vertically.
Therefore, we get the following equations:
58.5 N = Weight of the child + Normal force (vertical)
0 N = Normal force (horizontal)
From the second equation, we can conclude that the normal force is 0 N in the horizontal direction. Therefore, the normal force only acts vertically.
Now, let's substitute the value of the normal force in the first equation:
58.5 N = Weight of the child + 0 N
Simplifying the equation, we get:
Weight of the child = 58.5 N - 0 N
Weight of the child = 58.5 N
So, the weight of the child is 58.5 N.
Now, since the normal force only acts vertically, and we found that it is 0 N in the horizontal direction, it means that the magnitude of the normal force acting on the sled is also 0 N.