A ball of mass 0.150 kg is dropped from rest

Sam Longoria 2021-12-18 Answered
A ball of mass 0.150 kg is dropped from rest from a height of 1.25 m. It rebounds from the floor to reach a height of 0.960 m. What impulse was given to the ball by the floor?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

sukljama2
Answered 2021-12-19 Author has 33 answers
Step 1
In this problem, a ball of mass m=0.150m is dropped from a rest height of h1=1.25m. If rebounds from the floor to reach of h2=0.960m. We calculate the impulse given to the ball by the floor. We use g=9.80ms2
Step 2
Let the upward direction be positive. Initially, the ball moves downwards, so the initial momentum is negative. Using conservation of energy, we have
KEi+PEi=KEf+PEf
0+mgh1=mv122+0
mgh1=m2v122m
mgh1=p122m
p12=2m2gh1
p1=2m2gh1
p1=2m2gh1
Step 3
Similarly, after the rebound, the momentum must be
p2=+2m2gh2
Step 4
The impulse must be
I=p2p2
=+2m2gh2(2m2gh1)
=2m2gh2+2m2gh1
=2m2g(h2+h1)
=[2(0.150kg)2(9.80ms2)](0.960m+1.25m)
=+1.39312N×s
I=+1.39N×s
Since the impulse is positive, it must be upwards.

We have step-by-step solutions for your answer!

Becky Harrison
Answered 2021-12-20 Author has 40 answers
When an object receives a force for a short time, this force with time is called the impulse, so it is the area under the curve of the force-versus-time graph and it is the same as the change in momentum. The impulse is the quantity I and it is given by equation (6.4) in the form
1) I=FΔt=mvfmvi
When the ball is dropped from a height of 1.25 m, it gains velocity due to the gravitational acceleration. This is the initial velocity before it hits the floor. From the kinematic equations, we can calculate this velocity by
2) vi2=v02+2gh0
vi=0+2gh0
The height is h0=1.25m Use this value into equation (2) to get the velocity of the ball before it drops on the floor
vi=2gh0=2(9.8ms2)(1.25m)=4.95ms
When the ball hits the floor, it changes its velocity. The final velocity could be calculated using equation (2) but for height, h=0.960m
vf=2gh=2(9.8ms2)(0.960m)=4.34ms
Now, we plug the values for m, vf and vi into equation (1)to get the impulse
I=mvfmvi
=(0.150kg)(4.34ms4.95ms)
=1.39kg×ms
The negative sign indicates that the direction of the impulse is upward.

We have step-by-step solutions for your answer!

nick1337
Answered 2021-12-27 Author has 575 answers

Step 1
By definition, the impulse given to the ball is equal to the change of its momentum:
J=Δp=m(v2v1)
where m=0.15kg is the mass of the ball,v1, v2 are the projections of the ball's velocity on the vertical axis before and after the collision respectively.
Let's direct the vertical axis upwnward.
According to the mechanical energy conservation, the kinetic energy of the ball right before the collision is equal to its potential energy at the begining of the motion. Writting down the corresponding formulas for these energies, obtian:
mv122=mgh1
where g=9.81m/s2 is the gravitational acceleration. and h1=1.25m is the initial height. Thus, obtain:
v1=2gh1
(negative, since before the collision the velocity is directed downward).
After the collision, the kinetic energy of the ball is equal to its potential energy at the maximum height h2=0.96m. Obtain:
mv222=mgh2
v2=2gh2
(positive, since after the collision the velocity is directed upward).
Finally, obtain the expression for the impulse:
J=m(v2v1)=m2g(h1+h1)
J=0.15×2×9.18×(1.25+0.96)1.39N×s

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-03-13
When a person stands on tiptoe (a strenuous position), the position of the foot is as shown in Figure (a). The total gravitational force on the body, vector F g, is supported by the force vector n exerted by the floor on the toes of one foot. A mechanical model of the situation is shown in Figure (b), where vector T is the force exerted by the Achilles tendon on the foot and vector R is the force exerted by the tibia on the foot. Find the values of vector T , vector R , and θ when vector F g = 805 N. (Do not assume that vector R is parallel to vector T .)
asked 2021-02-18
In an industrial cooling process, water is circulated through a system. If the water is pumped with a speed of 0.45 m/s under a pressure of 400 torr from the first floor through a 6.0-cm diameter pipe, what will be the pressure on the next floor 4.0 m above in a pipe with a diameter of 2.0 cm?
asked 2020-10-28
Hi I need help with thisquestion. A uniform metal rod, with a mass of 3.1 kg and a length of 1.2 m,is attached to a wall by a hinge at the base. A horizontalwire bolted to the wall 0.51 m above the base of the rod holds therod at an angle of 25 degrees above the horizontal. The wireis attached to the top of the rod. (a) Find the tension inthe wire. (b) Find the horizontal and verticalcomponents of the force exerted on the rod by the hinge. Thank you
asked 2021-02-19
Three Children are trying to balance on a seesaw, which consists of a fulcrum rock, acting as a pivot at the center, and avery light board 3.6 m long. Two playmates are already on either end. Boy A has a mass of 50kg, and girl B a mass of 35 kg. Where should girl C, whose mass is 25 kg, placed herself so as to balance the seesaw.
asked 2021-12-06

I am having trouble setting up this question. Am I on the right path?
L{f(t)}=02πtestdt

asked 2021-02-13
A person exerts a horizontal force of 190 N in the testapparatus shown in the figure. Find the horizontal force that his flexormuscle exerts on his forearm.
asked 2021-01-31
A motorist travels for 3.0h at 80.0 km/h and 4.0 h at 60.0km/h. What is her average speed for the trip?

New questions

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question