Question

TASK 1:

given:

Weight of roller W in Newtons = 2.75 N

Weight of pan W_P in Newtons   = 0.25 N

a. Calculate average value m_avg(g) in this table

α (°)	mmin(g)	mmax(g)	mavg(g)
10°	11	20
20°	60	75
30°	99	125
40°	140	170

b. Determine the force along the plane F₁ from measurement using    and plot the graph F₁(N) versus sin(α) below using the indicated scale (10%) Table + (10%) Graph.

c. Use the slope found on graph and the (F_1=W∙sin(α) to find out the weight W of the roller from the graph.

d.Compare the weight of the roller directly measured by the dynamometer and the value obtained from the graph. Which one is more reliable? Explain

Answer 1

Task 1
given
weight of roller in Newtons, 2.75 N
weight of pan in Newtons, 0.25 N

a. filled table with average m is as under
here mavg = (mmin + mmax)/2
here we have some other columns as well
alpha in radians is found by using apha in rad = alpha in deg *pi()/180
m avg kg = m avg g /1000
and F1 in newtons is m avg in kg (9.81 where 9.81 is accelration due to gravity in m/s/s)

alpha (deg)	alpha (rad)	m min (g)	m max (g)	m avg (g)	m avg (kg)	sin(alpha)	F1 (N)
10	0.174532925	11	20	15.5	0.0155	0.173648	0.152055
20	0.34906585	60	75	67.5	0.0675	0.34202	0.662175
30	0.523598776	99	125	112	0.112	0.5	1.09872
40	0.698131701	140	170	155	0.155	0.642788	1.52055

  

b. the graph between F and sin(alpha) is as under

from the slope

m = 2.9021
c.
but, slope is ratio of F and sin(alpha)
now,
F/sin(alpha) = W
from graph W = 2.9021 N
weight of roller is W - 0.25 = 2.6521 N
  
d. from the graph weight is 2.6521 N , and from dynamometer weight is 2.75 N
since we have multiple errors in our experiment, where as dynamometer is a specifically designed instrument for measring force (weight) hecne dynamometer is more reliable