A shopping cart full of groceries with a total mass (m) movesdown the aisle at a

Question

A shopping cart full of groceries with a total mass (m) movesdown the aisle at a speed (v). The cart is then stopped by aconstant force F.    a. Use the impluse-momentum relationship andshow that the time required to stop the cart is mv/F.    b. If the total mass of the cart is 20.0 kg,its initial speed is 3.0 m/s, and the stopping force is 15.0 N,show that the stopping time is 4.0s.    c. Show that the initial kinetic energy ofthe loaded shopping cart was 90 J. A shopping cart full of groceries with a total mass (m) movesdown the aisle at a speed (v). The cart is then stopped by aconstant force F.    a. Use the impluse-momentum relationship andshow that the time required to stop the cart is mv/F.    b. If the total mass of the cart is 20.0 kg,its initial speed is 3.0 m/s, and the stopping force is 15.0 N,show that the stopping time is 4.0s.    c. Show that the initial kinetic energy ofthe loaded shopping cart was 90 J.

Explanation / Answer

A shopping cart full of groceries with a total mass (m) movesdown the aisle at a speed (v). The cart is then stopped by aconstant force F.    a. Use the impluse-momentum relationship andshow that the time required to stop the cart is mv/F.    b. If the total mass of the cart is 20.0 kg,its initial speed is 3.0 m/s, and the stopping force is 15.0 N,show that the stopping time is 4.0s.    c. Show that the initial kinetic energy ofthe loaded shopping cart was 90 J.
impulse=change in momentum=mv-mu impulse=force *time so force *time=mv-mu F*t=mv-mu time=[mv-mu]/F the initial speed of cart=v when it is stopped v=0 the change in momentum=mv so Time t=mv/F substituting the numericals we get t=20*3/15=4sec initial kinetic energy=1/2 mv*v=1/2*20*3*3=90J

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