A uniform hollow spherical ball of mass 1.75 kg and radius 40.0 cm rolls without slipping up a ramp that rises at 30.0° above th
1 answer:
Answer:
The acceleration of the ball's center of mass = 2.94 m/s²
Explanation:
The speed of the ball at the base of the ramp, v = 2.63 m/s
Mass of the ball = 1.75 kg
Radius of the ball, R = 40 cm = 0.4 m
In this motion, potential energy due to the height of the ball is converted to linear angular kinetic energy
Based on the law of energy conservation
Potential energy = Linear KE + angular KE
KE = kinetic Energy
Linear KE = 0.5 mv²
Linear KE = 0.5 * 1.75 * 2.63²
Linear KE = 6.052 J
Angular KE = 0.5 Iω²
I = 2/ 3 MR² = 0.667 * 1.75 * 0.4²
I = 0.187 N.s
ω = V/R = 2.63/0.4
ω = 6.575 Rad/s
Angular KE = 0.5 * 0.187 * 6.575²
Angular KE = 4.04 J
PE = mgh = 1.75 * 9.8 * h = 17.15h
Using the law of energy conservation
17.15h = 6.052 + 4.04
h = 10.092/17.15
h = 0.589 m
Using the equation of motion
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Ans:
1. τbiceps = +(Positive)
2. τforearm = -(Negative)
3. τball = -(Negative)
Explanation:
The figure is attached down below.
1. T<span>orque about the elbow caused by the biceps, τbiceps:
Since Torque = r x F (where r and F are the vectors)
</span>Where r is the vector from elbow to the biceps.
<span>
We can see in the figure that F(biceps) is in upward direction, and by applying the right hand rule from r to F, we get the counterclockwise direction. The torque in counterclockwise direction is positive(+). Therefore, the sign would be +.
2. </span>Torque about the the weight of the forearm, τforearm:
Since Torque = r x F (where r and F are the vectors)
Where r is the vector from elbow to the forearm.
Also weight is the special kind of Force caused by the gravity.
We can see in the figure that W(forearm) is in downward direction, and by applying the right hand rule from r to F, we get the clockwise direction. The torque in clockwise direction is negative(-). Therefore, the sign would be -.
3. Torque about the the weight of the ball, τball:
Since Torque = r x F (where r and F are the vectors)
Where r is the vector from elbow to the ball.
Also weight is the special kind of Force caused by the gravity.
We can see in the figure that W(ball) is in downward direction, and by applying the right hand rule from r to F, we get the clockwise direction. The torque in clockwise direction is negative(-). Therefore, the sign would be -.
1. τbiceps = +(Positive)
2. τforearm = -(Negative)
3. τball = -(Negative)
Explanation:
The figure is attached down below.
1. T<span>orque about the elbow caused by the biceps, τbiceps:
Since Torque = r x F (where r and F are the vectors)
</span>Where r is the vector from elbow to the biceps.
<span>
We can see in the figure that F(biceps) is in upward direction, and by applying the right hand rule from r to F, we get the counterclockwise direction. The torque in counterclockwise direction is positive(+). Therefore, the sign would be +.
2. </span>Torque about the the weight of the forearm, τforearm:
Since Torque = r x F (where r and F are the vectors)
Where r is the vector from elbow to the forearm.
Also weight is the special kind of Force caused by the gravity.
We can see in the figure that W(forearm) is in downward direction, and by applying the right hand rule from r to F, we get the clockwise direction. The torque in clockwise direction is negative(-). Therefore, the sign would be -.
3. Torque about the the weight of the ball, τball:
Since Torque = r x F (where r and F are the vectors)
Where r is the vector from elbow to the ball.
Also weight is the special kind of Force caused by the gravity.
We can see in the figure that W(ball) is in downward direction, and by applying the right hand rule from r to F, we get the clockwise direction. The torque in clockwise direction is negative(-). Therefore, the sign would be -.