Question

Karla, Matthew, Danielle, Vince, and Sergio all have carts of different masses. In their lab, they each apply a different amount of force to their carts, resulting in different accelerations. However, they did not label their data table and are now trying to backtrack and identify all of their data. Your task: using the clue below and your understanding of Newton's 2nd Law of Motion, help each student determine the mass and/or acceleration of their and the force they each gave to their cart.

1. Danielle pushed her cart with a force 15 Newtons and it accelerated 2.5 m/s2. If Karla's cart has twice as much mass as Danielle's, what is the mass of Karla's cart?

Answer 1

Answer:

Explanation:

Background story: Karla, Matthew, Daneisha, Vince and Sergio all have carts of different masses. In

their lab, they each apply a different amount of force to their carts, resulting in different accelerations.

Yikes! They did not label their data table and are now trying to backtrack and identify all of their data.

Your task: using the clues below and your understanding of Newton’s 2nd Law of Motion (F=ma), help

each student determine the mass of their cart, the acceleration of their cart, and the force they each gave

their cart.

What the students know:

• the carts had masses of 6 kg, 4.5 kg, 9 kg, 10 kg and 12 kg

• the carts had accelerations of 5 m/s2

, 3 m/s2

, 2 m/s2

, 4 m/s2

, and 2.5 m/s2

Clues:

1) Karla’s cart is half the mass of Daneisha’s cart.

2) The mass of Vince’s cart is neither the smallest nor the largest.

3) The mass of Sergio’s cart is greater than the mass of Vince’s cart.

4) The acceleration of Daneisha’s cart was half the acceleration of Sergio’s cart.

5) The force Vince applied to his cart was larger than the force that Matthew applied to his cart.

6) The acceleration of Matthew’s cart was greater the acceleration of Vince’s cart.

7) Karla applied less than 18 N of force to her cart.

8) Sergio applied more than 40 N of force to his cart.

9) Daneisha applied more than 27 N of force to her cart.

10) The acceleration of Vince’s cart was greater than the acceleration of Daneisha’s cart.

11) The acceleration of Karla’s cart was less than the acceleration of Vince’s cart.

12) Karla applied the least amount of force to her cart.

13) Vince’s cart had twice the mass of Matthew’s cart.

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Answer 2

Given: Danielle pushed her cart with a force 15 Newtons and it accelerated 2.5 m/s2.

To find: We have to find the mass of Karla's car.

Solution:

We know that according to Newton's second law force=mass×acceleration

Now the force need to push Danielle's cart is 15N.

It acceleration is $2.5m/s^2$.

So, mass of Danielle's car is-

$\frac{15}{2.5} = 6$

Now given that Karla's cart has twice as much mass as Danielle's. To determine mass of Karla's cart multiple 6 with 2.

So,mass of Karla's cart is =2×6=12kg.