A man opens a 1.14-m wide door by pushing on it with a force of 49.5 N directed perpendicular to its surface.
(a) What magnitude torque does he apply about an axis through the hinges if the force is applied at the center of the door?
N · m
(b) What magnitude torque does he apply at the edge farthest from the hinges?
N · m
For part a Torque T= F *r
T= 49.5 N * 1/2(1.14 m) =28.215 Nm
Sorry I'm still trying to find part b as well...
Ok here's part B:
T= F* r
T=1.14 m *49.5 cuz now theyre asking for the whole door not just the center
T= 56.43
(a) Well, opening a door can be quite a chore, but luckily torque is here to help us out! To calculate the torque that the man applies when pushing at the center of the door, we can use the equation torque = force * distance. Since the force is applied perpendicular to the door's surface, the distance from the center to the hinges is half the width of the door, or 1.14/2 = 0.57 m. Plugging in the values, we get torque = 49.5 N * 0.57 m = 28.22 N · m. So he applies a torque of 28.22 N · m about the axis through the hinges.
(b) Now, when the man pushes on the edge farthest from the hinges, things get a little more interesting! The force is still perpendicular to the door's surface, but now the distance changes. The new distance from the edge to the hinges is the full width of the door, so 1.14 m. Plugging in the values again, torque = 49.5 N * 1.14 m = 56.43 N · m. So he applies a torque of 56.43 N · m at the edge farthest from the hinges.
So there you have it, the man applies a torque of 28.22 N · m about the hinges when pushing at the center, and a torque of 56.43 N · m at the edge farthest from the hinges. Now that's some twisting action!
To solve this problem, we need to use the formula for torque: torque = force x lever arm.
(a) When the force is applied at the center of the door, the torque is given by:
torque = force x lever arm
The lever arm is half the width of the door, since the force is applied at the center:
lever arm = 1.14 m / 2 = 0.57 m
Substituting the values into the formula:
torque = 49.5 N x 0.57 m
Calculating the torque:
torque = 28.215 N·m
Therefore, the magnitude of the torque when the force is applied at the center is 28.215 N·m.
(b) When the force is applied at the edge farthest from the hinges, the lever arm is the full width of the door:
lever arm = 1.14 m
Using the formula for torque:
torque = force x lever arm
Substituting the values:
torque = 49.5 N x 1.14 m
Calculating the torque:
torque = 56.43 N·m
Therefore, the magnitude of the torque when the force is applied at the edge farthest from the hinges is 56.43 N·m.
To calculate the torque, we need to first determine the distance of the force from the axis of rotation. In this case, the axis of rotation is through the hinges.
(a) When the force is applied at the center of the door, it is at a distance equal to half of the width of the door (1.14 m / 2 = 0.57 m) from the axis of rotation.
To calculate the torque, we can use the formula:
Torque = Force x Distance
Substituting the given values:
Torque = 49.5 N x 0.57 m
Torque = 28.215 N · m
So, the man applies a torque of 28.215 N · m about an axis through the hinges when the force is applied at the center of the door.
(b) To calculate the torque when the force is applied at the edge farthest from the hinges, we need to find the distance of the force from the axis of rotation.
Since the force is being applied at the edge farthest from the hinges, the distance from the axis of rotation is equal to the width of the door, which is 1.14 m.
Using the same formula, the torque can be calculated as:
Torque = Force x Distance
Torque = 49.5 N x 1.14 m
Torque = 56.43 N · m
Therefore, the man applies a torque of 56.43 N · m at the edge farthest from the hinges.