Sand from a stationary hopper falls on a moving conveyor beltat the rate of 5.70

Question

Sand from a stationary hopper falls on a moving conveyor beltat the rate of 5.70 kg/s as in thefigure below. The conveyor belt is supported by frictionlessrollers and moves at a constant speed of v = 0.690 m/s under the action of a constanthorizontal external force Fvectorext supplied by themotor that drives the belt. (a) Find the sand's rate of change of momentumin the horizontal direction.
1 N

(b) Find the force of friction exerted by the belt on the sand.
2 N

(c) Find the external force Fvectorext.
3 N

(d) Find the work done byFvector ext in 1 second.
4 J

(e) Find the kinetic energy acquired by the falling sand eachsecond due to the change in its horizontal motion.
5 J

(f) Why are the answers to parts (d) and (e) different?
6 Sand from a stationary hopper falls on a moving conveyor beltat the rate of 5.70 kg/s as in thefigure below. The conveyor belt is supported by frictionlessrollers and moves at a constant speed of v = 0.690 m/s under the action of a constanthorizontal external force Fvectorext supplied by themotor that drives the belt. (a) Find the sand's rate of change of momentumin the horizontal direction.
1 N

(b) Find the force of friction exerted by the belt on the sand.
2 N

(c) Find the external force Fvectorext.
3 N

(d) Find the work done byFvector ext in 1 second.
4 J

(e) Find the kinetic energy acquired by the falling sand eachsecond due to the change in its horizontal motion.
5 J

(f) Why are the answers to parts (d) and (e) different?
6 (a) Find the sand's rate of change of momentumin the horizontal direction.
1 N

(b) Find the force of friction exerted by the belt on the sand.
2 N

(c) Find the external force Fvectorext.
3 N

(d) Find the work done byFvector ext in 1 second.
4 J

(e) Find the kinetic energy acquired by the falling sand eachsecond due to the change in its horizontal motion.
5 J

(f) Why are the answers to parts (d) and (e) different?
6

Explanation / Answer

   from the given problem we can see that the sand isfalling continuosly and the stationary hopper    is moving with a velocity v = 0.690 m / s    so after one second the stationary hopper differs byshowing 5.70 kg of sand moving on the belt (a)    the sand's rate of change of momentum in thehorizontal direction will be    px / t = (5.70 kg)(0.690 m / s) / (1.00 s)                 = ........ N (b)    from the given we can see that the only horizontalforce on the sand is the belt friction    so that    pxi + f t = pxf    f = px / t      = ........ N (c)    when the belt is in equilibrium    Fx = m ax    Fext - f = 0    Fext = f           = ........N (d)    the work done will be    W = F r cos         = F (0.690 m)cos0o         = ......... J (e)    the kinetic energy is given by    (1 / 2) (m) v2 = (1 / 2) (5.70kg) (0.690 m / s)2                           = ......... J (f)    the firction between the sand and the belt convertshalf of the input work into extra internal    energy

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.