1.
The potential energy for a force field F is given by
U(x, y) = sin (x + y). The force acting on the par-
ticle of mass m at
Answers
Answered by
3
Answer:
Answer:
→
F
(
x
,
y
)
=
−
∇
U
(
x
,
y
)
F
(
x
,
y
)
=
|
∇
U
(
x
,
y
)
|
;
F
(
0
,
π
4
)
=
1
Explanation:
→
F
(
x
,
y
)
=
−
∇
U
(
x
,
y
)
∇
U
(
x
,
y
)
=
∂
U
∂
x
ˆ
x
+
∂
U
∂
y
ˆ
y
=
cos
(
x
+
y
)
(
ˆ
x
+
ˆ
y
)
F
(
x
,
y
)
=
|
∇
U
(
x
,
y
)
|
F
(
0
,
π
4
)
=
∣
∣
∇
U
(
0
,
π
4
)
∣
∣
=
∣
∣
cos
(
π
4
)
∣
∣
|
ˆ
x
+
ˆ
y
|
F
(
0
,
π
4
)
=
1
√
2
√
1
2
+
1
2
=
1
unit
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