Download Forces and acceleration Newton`s 2nd Law

Newton's 2nd Law
Physical Science 101
Newton's 2nd Law
11/96
Name ___________________________
Partner’s Name ___________________
Purpose
To explore and understand Newton's 2nd law of motion, which relates the net
force applied to an object to the objects mass and acceleration.
Equipment
photogate timer, cart, track, weights, weight hangers, and string
Set up the cart, track, photogate timer and weights as shown below.
card
cart
photogate
Pulley
weights
cushion
stool
There should be at least one card length between
the weights and cushion when the card is ready
to pass through the timer.
Measure the mass of the cart. Mcart = _______________ kg
Measure the length of the card x = ________________ m
Part A:
Purpose: To study how acceleration is related to force when the mass of a system is
kept constant.
Hang 20 g onto the string (weights and hanger) and put 40 g into the cart. The
mass that we will be accelerating in this activity is the total mass of the cart (including
loose masses) and hanger masses. To keep the mass of the system constant while
varying the force (hanger weight) we will just move mass from the cart to the hanger.
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Newton's 2nd Law
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What is the total mass of the cart plus weights system? Mtot=____________
With 20 g (0.020 kg) of mass on the hanger what is the accelerating force
(weight of the hanger)? Remember
F= w = mg
F = _____________ N
You want to pull the cart back so the hanger lifts off the cushion 20 or 30 cm,
release the cart, and measure its acceleration as it falls.
To do this:
** Pull the cart back to the position required to lift the hanger off the cushion by
20 or 30 cm.
** Position the photogate so that it's right next to the leading edge of the card.
The photogate should be in gate mode. Press the reset button to reset the time to zero.
** Slowly ease the cart forward (not letting it go) so that it starts the photogate
(red light on) and then back the cart up just enough so the timer stops running (or red
light off). If you put your finger in front of the cart so it just touches the cart and track,
you can roll your finger forward or backward for fine tuning the position. The cart
should now be in a perfect position for our acceleration measurement. Reset the timer.
When we let the cart go, being careful not to push it upon release, it will
immediately trigger the photogate timer. The timer will stop when the cart gets through.
Since the initial velocity is zero, we can use the formula
x
1 2
at
2
or
a
2x
2
t
to calculate a from the card length x and the time t.
Since the time is easy to measure, repeat the measurement three times and take an
average.
Do this for the 20 g weight and repeat for 40 g and 60 g. Remember take weights
from the cart and put them on the hanger so the total mass stays the same. Fill in the
table below, where Force is the accelerating force (hanger masses times g) and the
2x
acceleration is calculated using the above equation, a  2 .
t
The term M in F=Ma is the total of all masses cart + hanger.
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Newton's 2nd Law
System
Mass (kg)
m, hanger
mass (kg)
Force
mg (N)
time 1
(sec)
time 2
(sec)
11/96
time 3
(sec)
time avg
(sec)
Acc (2x/t2)
(m/s2)
By what factor does the acceleration change when you double the force?
Triple the force?
Although we accounted for the force of gravity pulling on the hanging mass, there
are often other forces in the system which may cause the acceleration to be different from
what you expect. Compare by calculating the percent difference in the calculated and net
forces.
F weight =
F net =
Fweight - Fnet
%difference = ------------------------------------ x 100% =
Fweight
Part B:
Purpose: To study how the acceleration is affected by the mass when the force is
kept constant. Repeat the above sort of experiment except this time use a constant
hanger mass of 60 g and change the system mass from 1(M cart + 60 g) to 2(Mcart + 60
g), and to 3(Mcart + 60 g). The black rectangular bars are close to the mass of the cart
alone. Fill in the table below. Your first entry can be the last entry from the table in part
B so you really only need to do two acceleration measurements to complete this table.
Again, Force is the accelerating force (hanger masses times g) which is the same for all
three trials.
With 60 g (0.060 kg) of mass on the hanger what is the accelerating force
(weight of the hanger)? Remember
F= w = mg
F = _____________ N
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Net
(Acc/Mas
Newton's 2nd Law
11/96
2x
, and the term M in
t2
F=Ma is the total of all masses (cart + hanger+masses in cart and on hanger).
The acceleration is calculated using the above equation, a 
System
Mass (kg)
m, hanger
mass (kg)
Force
mg (N)
time 1
(sec)
time 2
(sec)
time 3
(sec)
time avg
(sec)
Acc (2x/t2)
(m/s2)
By what factor does the acceleration change when you double the system mass?
Triple the mass?
For the largest mass, 3(Mcart + 60 g), calculate the theoretical acceleration using
F = M a.
Compare this to your experimentally measured value of a above.
a theory =
a exp =
%error 
atheory  aexp
atheory
x100 
Keeping in mind the net force comparison above, can you account for the difference with
the difference in net force?
What other forces are contributing to the net force?
Questions. Don't forget your units.
1. How much net force is required to give a 20.0 kg car an acceleration of 4.0 m/s2?
2. What is the mass of a girl who accelerates at a rate of 8.0 m/s2 when a net force of 56.0 N acts on
her?
3. What net force is required to accelerate a 0.5 kg ball from rest to a speed of 30.0 m/s in 0.5 sec?
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Newton's 2nd Law
11/96
(Hint: first find a using a=∆V/t)
4. What is the acceleration of a 30.0 kg boy when a net force of 60 N acts on him in the downward
direction?
5. What is the weight of a 30.0 kg boy?
6. If the boy in the above two questions is falling through the air in a parachute, what is the upward
force that the parachute exerts on the boy? Hint: the net force is 60 N down but the boy weighs 300 N.
How big must the air resistance force be to cancel all but 60 N of the boy’s weight?
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