In order to handle a hot pizza of mass 1.0 kg, a cook slides a
light (i.e., of negligible mass) but stiff spatula of length 2.0 m
from the right hand to the center of the pizza, which he then
carries horizontally with both hands. His right hand is at one
end of the pole (point A); his left hand is at a distance 0.50 m
farther down the pole (point B); and the pizza is at the other
end.
a. Draw a diagram of the spatula showing the forces acting on it. Make sure to label
the force vectors and to draw them with correct approximate lengths. [You will
need to solve parts b and c of this problem to determine these lengths.]
b. Determine the force exerted by the left hand on the spatula at point B.
c. Determine the force exerted by the right hand on the spatula at point A.
d. In which direction is the force exerted by the right hand?
a. To determine the forces acting on the spatula, we first need to visualize the situation described. Let's draw a diagram of the spatula, with point A being the right hand, point B being the left hand, and the pizza at the other end.
```
A B Pizza
----------------------------------------------------------- ← spatula (2.0 m)
```
Now, let's label the force vectors. We have the weight (W) of the pizza acting downward, the force exerted by the right hand (F_R) at point A, and the force exerted by the left hand (F_L) at point B.
```
F_R
A B Pizza
----------------------------------------------------------- ← spatula (2.0 m)
F_L
W
```
Remember that the length of the spatula is 2.0 m and the mass of the pizza is 1.0 kg.
b. To determine the force exerted by the left hand on the spatula at point B, we need to consider the torque balance. Since the spatula is held horizontally, there is no rotation, which means the sum of the torques must be zero.
The torque exerted by the right hand at point A is F_R multiplied by the length of the spatula (2.0 m). The torque exerted by the left hand at point B is F_L multiplied by the length of the spatula (2.0 m), but since it's exerted in the opposite direction, it will have a negative sign.
So we have:
Torque_A + Torque_B = 0
F_R * 2.0 m - F_L * 2.0 m = 0
Since the left hand is at a distance 0.50 m farther down the pole, the right hand is at a distance of 1.50 m from the left hand.
F_R * 2.0 m - F_L * 2.0 m = 0
F_R * 2.0 m - F_L * 1.5 m = 0
Solving for F_L, we get:
F_L = (F_R * 2.0 m) / (1.5 m)
c. To determine the force exerted by the right hand on the spatula at point A, we need to consider the overall force balance in the vertical direction. Since the spatula is held horizontally, there is no vertical acceleration, which means the sum of the vertical forces must be zero.
The force exerted by the left hand at point B and the weight of the pizza are acting downward, while the force exerted by the right hand at point A is acting upward.
So we have:
F_L + W - F_R = 0
Simplifying this equation for F_R, we get:
F_R = F_L + W
d. The force exerted by the right hand is directed upward.
a. As an AI text-based bot, I am unable to create visual or graphical representations. However, I can describe the forces acting on the spatula in a written form.
In this scenario, to handle the hot pizza, the forces acting on the spatula are as follows:
1. The weight of the spatula (W): This force acts vertically downwards from the center of the spatula.
2. The normal force exerted by the pizza on the spatula (Np): This force acts vertically upwards from the pizza at the end of the spatula.
3. The force exerted by the left hand (Fb): This force acts horizontally to the right at point B, towards the center of the spatula.
4. The force exerted by the right hand (Fa): This force acts horizontally to the left at point A, away from the center of the spatula.
b. To determine the force exerted by the left hand on the spatula at point B, we need to consider the equilibrium of forces in the horizontal direction. Since the spatula is not accelerating horizontally, the sum of horizontal forces must be zero.
The force exerted by the left hand at point B (Fb) is equal in magnitude but opposite in direction to the force exerted by the right hand at point A (Fa).
Therefore, the force exerted by the left hand at point B is equal to the force exerted by the right hand at point A.
c. Based on the explanation in part b, the force exerted by the right hand at point A (Fa) is equal in magnitude but opposite in direction to the force exerted by the left hand at point B (Fb).
d. The force exerted by the right hand at point A is directed horizontally to the left, away from the center of the spatula.