Calculating Velocity & Retarding Force of Dropped Mass

[Apothem]

Homework Statement

"A metal ball of mass 0.50 kg is dropped from the top of a vertical cliff of height 90m. When it hits the beach below it penetrates at a depth of 6.0cm. Calculate:
a) the velocity of the ball just as it hits the sand
b) the (average) retarding force of the sand

Homework Equations

SUVAT equation: v²=u²+2as
Newton's Second Law: F=ma

The Attempt at a Solution

For part a) I used suvat (s=90m, u=0ms^-1, v=v ,a=9.81ms^-2 , t=t) and used the suvat equation to calculate the final velocity as 42ms^-1

For part b) I am unsure, do I just use F=ma (with m=0.50kg and a=9.81ms^-2) to get an answer of 4.91N, or am I missing something?

 

[cepheid]

Homework Statement

"A metal ball of mass 0.50 kg is dropped from the top of a vertical cliff of height 90m. When it hits the beach below it penetrates at a depth of 6.0cm. Calculate:
a) the velocity of the ball just as it hits the sand
b) the (average) retarding force of the sand

Homework Equations

SUVAT equation: v²=u²+2as
Newton's Second Law: F=ma

The Attempt at a Solution

For part a) I used suvat (s=90m, u=0ms^-1, v=v ,a=9.81ms^-2 , t=t) and used the suvat equation to calculate the final velocity as 42ms^-1

For part b) I am unsure, do I just use F=ma (with m=0.50kg and a=9.81ms^-2) to get an answer of 4.91N, or am I missing something?

For part b, no, it's not just the case that a = g. That would be true only if the object were in free fall (meaning gravity is the only force acting). Once it hits the ground and starts burrowing, this is no longer true. There is another force (from the ground).

What you have to do is apply the same equation as you did for part a, this time with u = the v you calculated from part a, and v = 0 since it comes to rest. From this you can figure out what acceleration is *required* in order to slow the object down over that distance. This required acceleration tells you the net force.

 

[Tanya Sharma]

Homework Statement

"A metal ball of mass 0.50 kg is dropped from the top of a vertical cliff of height 90m. When it hits the beach below it penetrates at a depth of 6.0cm. Calculate:
a) the velocity of the ball just as it hits the sand
b) the (average) retarding force of the sand

Homework Equations

SUVAT equation: v²=u²+2as
Newton's Second Law: F=ma

The Attempt at a Solution

For part a) I used suvat (s=90m, u=0ms^-1, v=v ,a=9.81ms^-2 , t=t) and used the suvat equation to calculate the final velocity as 42ms^-1

For part b) I am unsure, do I just use F=ma (with m=0.50kg and a=9.81ms^-2) to get an answer of 4.91N, or am I missing something?

Part a) is alright .

For Part b) the ball starts with an initial velocity 42ms^-1 and ends up being at rest covering a distance of 6.0 cm .During the motion the ball is under the influence of two forces,force of gravity and the retarding force of the sand .Using F=Ma with a=9.81 is incorrect. Value of 'a' can be calculated using SUVAT equations .Now using F=Ma will give you the net force .

 

[CWatters]

You should find that a > g due to the very short stopping distance.