How High Does a Stone Reach When Shot from a Slingshot?

In summary: For the second question, you found the potential energy correctly but for the second part, you forgot to use the conservation of energy equation [itex]KE_{top} + PE_{top} = KE_{bottom} + PE_{bottom}[/tex] For the third question, you found the potential energy correctly but you forgot to take into account the work done by friction, which would be equal to the change in kinetic energy. Therefore, the work done by friction is 8100J. For the fourth question, you correctly found the potential energy and used the conservation of energy equation to find the maximum speed. To calculate the work done by friction, you would need to use the same equation as in the third question, where
  • #1
Aka
12
0
i have a test tomorow and I am having trouble with these questions can some one pls check over my answers?
1. a slingshop shoots a 12g stone at 36m/s. It goes in an arc and at the top of the arc it is going at 14m/s. How high is it at this point?
12g=0.012kg
36m/s=v1
14m/s=v2
Ek=1/2mv2
=1/2(0.012kg)(36m/s)2
=0.216J
Eg=mgh
0.216=0.012kg(9.8m/s)h
0.216J
0.1176
=1.8m
the hight is 1.8m
2. A child of 27kg climbs to the top of a 5.0m high playground slid
A) what is her potentian energy?
27kg=m
5.0m=h
Eg=mgh
=27kg(9.8m/s)(5.0m)
=1323J
the potential energy is 1323J
B)Her actual speed at the bottom is only 3m/s. According to conservation of energy how fast should se be going?
Ek=1/2mv2
=1/2(27kg)v2
1323/13.5=v2
98=v2
9.9=v
she should be going 9.9m/s
C) the slid is 8.0m long. determine the force of friction acing
d=8.0m
Ff=?
d=(v2+v1/2)t
t=1.6s
a=v2-v1/t
a=9.9m/s-0m/s/1.6s
a=6.2m/s2
F=ma
27kg(6.2m/s2)
F=167.4N
the force of friction is 167.4N
3. A 72kg passenger is in a van moving at 15m/s when it colides with a wall. The frount part of the van collapses 0.50m during the crash. determine the work done on the passenger and the force the seatbelt exerts during the acident.
72kg=m
15m/s=v1
0.50m=d
w=?
Ff=?
Ek=1/2mv2
=1/2(72kg)(15m/s)2
=8100J
...now what?
4/ A roler coaster has a height of 94.5m above the ground at its highest point. deteremine the maximum speed of the cars as they come down from this high point. the actual speed is 41.1m/s. Calcuate the work done by friction.
Eg=mgh
=1kg(9.8m/s2)(94.5m)
=926.1J
Ek=1/2mv2
926.1=1/2(1kg)v2
926.1/0.5=v2
1852.2=v2
43m/s=v
the maximun speed it 43m/s
i don't know how to calculate the force of friction
 
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  • #2
For the first question you forgot to take into account the fact that the projectile still has kinetic energy at the top so [itex]PE_{top} = KE_{bottom} - KE_{top}[/tex]
 
  • #3
in this scenario without more information about the roller coaster's design and the materials used. It would also depend on the speed and direction of the cars and the angle of the track. It is not possible to accurately calculate the force of friction in this situation without more information.
 

Related to How High Does a Stone Reach When Shot from a Slingshot?

1. What is kinematics in the context of a slingshot?

Kinematics refers to the study of motion, specifically in terms of position, velocity, and acceleration. In the context of a slingshot, kinematics would involve analyzing the movement of the slingshot and its projectile.

2. How does the slingshot's design impact its kinematics?

The design of the slingshot, including its materials, shape, and tension, can greatly affect its kinematics. These factors can impact the force applied to the projectile, the angle of release, and the speed and trajectory of the projectile.

3. Is there a maximum range for a slingshot based on its kinematics?

Yes, the maximum range of a slingshot is determined by its kinematics. Factors such as the angle of release, initial velocity, and air resistance can all affect the range of the projectile.

4. How do you calculate the velocity of a projectile launched from a slingshot?

The velocity of a projectile launched from a slingshot can be calculated using the equation v = √(2gh), where v is the velocity, g is the acceleration due to gravity, and h is the height of the slingshot at the point of release.

5. Can the kinematics of a slingshot be used to improve its accuracy?

Yes, by understanding the kinematics of a slingshot, one can make adjustments to its design or the way it is used to improve accuracy. Factors such as the angle of release, tension in the slingshot, and the shape and weight of the projectile can all be manipulated to increase accuracy.

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