[Chikis (OP)]

A towing van of mass 6.0 * 10^3 kg used in towing a car of mass m moved with a speed of 4ms^-1 just before the towing rope become taut. Calculate the

(i) value of m if the speed of the van reduced to 2.5 ms^-1 when the rope became taut.

(ii) loss in kinetic energy of the system after the car had started moving.

(iii) impulse in the rope when it jerked the car into motion.

I don't know what principle to apply in solving the problem. Somebody help me please.

[Pmb]

A towing van of mass 6.0 * 10^3 kg used in towing a car of mass m moved with a speed of 4ms^-1 just before the towing rope become taut. Calculate the

(i) value of m if the speed of the van reduced to 2.5 ms^-1 when the rope became taut.

(ii) loss in kinetic energy of the system after the car had started moving.

(iii) impulse in the rope when it jerked the car into motion.

I don't know what principle to apply in solving the problem. Somebody help me please.

It's our policy never to do someone's homework for them. At best will help you after you've taken a shot at solving it yourself, showing your work.

[Chikis (OP)]

This is my work:
Mv and Mc = mass of van and car respectively; Mvu = initial momentum of van; Mcu = initial momentum of car; Mvv and Mcv = final momentum of van and car respectively.

initial momentum = final momentum

Mvu + Mcu = (Mv + Mc)v

 6000*4 + 0*mc = 6000*2.5 + 2.5M

24000 = 15000 + 2.5Mc

24000- 15000 = 2.5Mc

9000 = 2.5Mc

Mc = 9000/2.5 = 3,600 kg

Do you agree with me?

[Chikis (OP)]

Kinetic energy before the rope become taut = 1/2 Mvu^2  + 1/2 Mcu^2 = 1/2 * 6000 * 16 + 1/2 * 3600 *0^2
= 48000 + 0
= 48000J

kinetic energy during the towing = 1/2 Mvv^2 + 1/2 Mcv^2 = 1/2 * 6000 * 2.5^2 + 1/2 * 3600 * 2.5^2 = 18750 + 11250 = 30000J
 
Change in kinetic energy = 48000 - 30000 = 18000J

[Chikis (OP)]

Impulse = change in momentum of the car

Impulse =  Mcv - McU
= 3600*2.5 - 3600*0
= 9000 Ns. What do you have to say cocerning my works?

[Pmb]

Impulse = change in momentum of the car

Impulse =  Mcv - McU
= 3600*2.5 - 3600*0
= 9000 Ns. What do you have to say cocerning my works?

It's very late right now. I'll read it over and get back to you in the morning.

[Pmb]

In the first place I congradulate you on desire to learn physics. It's well known to be the hardest thing on earth to master. Second, there is insufficient information to solve all but the mass of the car, which you did correctly. I recommend that the next time you first leave all the variables in until you do the final calculation. E.g. If M - mass of truck and m = mass of car, v_initial is the initial speed of truck and v_final is the final speed of the truck-car system then the mass of the car is m =(v_initial/v_final - 1)M = (4/2.5 - 1)6x10³kg = 3.6x10³kg.

You made an error in your calculation of kinetic energy loss. Please recheck your calculation. Since energy is a conserved quantity do you know where the kinetic energy went to?

The value for the impulse seems okay to me.

[Chikis (OP)]

In the first place I congradulate you on desire to learn physics. It's well known to be the hardest thing on earth to master. Second, there is insufficient information to solve all but the mass of the car, which you did correctly. I recommend that the next time you first leave all the variables in until you do the final calculation. E.g. If M - mass of truck and m = mass of car, v_initial is the initial speed of truck and v_final is the final speed of the truck-car system then the mass of the car is m =(v_initial/v_final - 1)M = (4/2.5 - 1)6x10³kg = 3.6x10³kg.

You made an error in your calculation of kinetic energy loss. Please recheck your calculation. Since energy is a conserved quantity do you know where the kinetic energy went to?

The value for the impulse seems okay to me.

I can hardly see any error in my calculation of kinetic energy loss. The collision is perfectly inelastic. The kinetic energy of the system before impact is greater than the kinetic energy after impact; because part of the kinetic energy has been dispensed in towing the car. Moreover, the initial momentum of the car is zero because the car has zero velocity. Where or what is my error in the calculation? Am eager to learn.

[Pmb]

I can hardly see any error in my calculation of kinetic energy loss.

You calculated the final kinetic energy to be 30000J but when you went to subtract it froom the initial kinetic energy of 48000 you mistakenly used 3000J leaving off a "0".

.. because part of the kinetic energy has been dispensed in towing the car.

The missing energy went into thermal energy and energy of deformation.

[Chikis (OP)]

I can hardly see any error in my calculation of kinetic energy loss.

You calculated the final kinetic energy to be 30000J but when you went to subtract it froom the initial kinetic energy of 48000 you mistakenly used 3000J leaving off a "0".

.. because part of the kinetic energy has been dispensed in towing the car.

The missing energy went into thermal energy and energy of deformation.

Now I got what you are saying. I thought that I had made a terrible mistake in my calculation. I hope apart from that mistake, I made no other error? I have simply corrected the error by modifying the post. Thank you.

The missing energy went into thermal energy and energy of deformation.

Do you mean the missing enery was used as energy of the deformation of the rope? What themal energy are you making refrence to? Thank you.

[Pmb]

Do you mean the missing enery was used as energy of the deformation of the rope? What themal energy are you making refrence to? Thank you.

When a rope is used to pull a car the rope extends a bit and that requires work which is changed into potential energy. That potential energy changes eventually into kinetic energy. The same thing is true for the car.

[Quantum Sausage]

A towing van of mass 6.0 * 10^3 kg used in towing a car of mass m moved with a speed of 4ms^-1 just before the towing rope become taut. Calculate the

(i) value of m if the speed of the van reduced to 2.5 ms^-1 when the rope became taut.

(ii) loss in kinetic energy of the system after the car had started moving.

(iii) impulse in the rope when it jerked the car into motion.

I don't know what principle to apply in solving the problem. Somebody help me please.

It depends what reference frame you're in

[Pmb]

A towing van of mass 6.0 * 10^3 kg used in towing a car of mass m moved with a speed of 4ms^-1 just before the towing rope become taut. Calculate the

(i) value of m if the speed of the van reduced to 2.5 ms^-1 when the rope became taut.

(ii) loss in kinetic energy of the system after the car had started moving.

(iii) impulse in the rope when it jerked the car into motion.

I don't know what principle to apply in solving the problem. Somebody help me please.

It depends what reference frame you're in

This is a problem in non-relativistic mechanics so your response does not apply here.